The term “Marriage Premium” (sometimes “Marital Premium”) most commonly refers to the seeming benefits (primarily) married men enjoy over unmarried men, though it also applies to the seeming benefits children with married parents enjoy over children whose parents are not married.
The first set of benefits seems to be accrued by men who are married and who thus (often, at least) benefit from the economic and lifestyle perks of cohabitation, traditionally (though not always) with a partner who takes care of the home, the children, and other (usually unpaid) labor that would otherwise fall on his shoulders alongside his paid work.
This is a stereotypical and not at all broadly representative collection of assumptions, of course, but they seem to also apply when the pronouns and specific nature of the work being done are altered.
The idea is that work/household division of labor, or bare-minimum having two sets of hands instead of just one, makes it more likely that whomever’s the more career-focused of the couple will climb the career ladder faster, earning more money and benefitting from a seeming bias toward married people in the workplace (possibly the result of assumed stability in married couples over unmarried individuals).
The “Marriage Gap” between folks who are married and unmarried differs from culture to culture, and even under different political administrations (as taxes, healthcare setups, social perceptions, and safety nets may vary depending on who’s in charge). But there does seem to be a fairly consistent distinction in both economic success and self-reported happiness, at least on average, between married people and those who are unmarried.
That said, recent research suggests that part of this effect might be related to a cultural bias that almost entirely disappears when marriage loses its normative status within a given society. And this seems to be true for married and unmarried adults, but also the premium enjoyed (or missed out on) by children, based on their parents’ marital situation (children of married couples tend to have advantages over children whose parents are not married).
Within a single generation, marriage went from being the norm to the exception in Chile. Babies born to married people in the early 1990s had substantial advantages across a range of metrics compared to kids who were born out of wedlock. But by the mid-2010s, that advantage had all but disappeared.
Researchers checked a series of possible causes for this change, and the only one that seems to explain the diminishment of this gap is the shift in common views toward marriage.
This finding suggests that the children of parents who are in some way outside the mainstream (including, for instance, homosexual couples in societies where heterosexuality is the norm, or perhaps even considered the only morally correct pairing) might experience disadvantages related to this abnormality (and distinct from other possible influences, like economic class and genetic inheritance).
The same might be true of the Marriage Premium enjoyed by (or denied) adult couples, though more research will need to be done to see if this finding translates in that way.